Anisotropic neutrino emission during the neutron star formation can be the origin of the observed proper motions of pulsars. We derive a general expression for the momentum asymmetry in terms of the neutrino energy flux gradient, and show that a nonvanishing effect is induced at the lowest order by a deformed neutrinosphere. In particular, this result is valid for a neutrino flux transported through a spherical atmosphere with constant luminosity.Comment: 11 pages, added appendix, references, and minor changes in section 1, 2, and

We develop a thorough description of neutrino oscillations in a magnetized protoneutron star, based on a resonance layer for neutrinos with different momentum directions. We apply our approach to the calculation of the asymmetry in the neutrino emission during the birth of a neutron star and the pulsar acceleration in the case of an active-sterile neutrino resonant conversion.The observed velocities can be obtained with the magnetic fields expected in the interior of a protoneutron star, for sterile neutrino masses of the order of KeV and small mixing angles. * Permanent address: Instituto Balseiro and CAB, Universidad Nacional de Cuyo and CNEA, 8400 Bariloche, Argentina 1

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